A battery is a battery of cells. A group of them. Smaller batteries that make "12" volts from six "2.2" volt cells are conveniently packaged in one case. Larger batteries, like those on fork lifts, have rather large individual cells that can be individually replaced if need be. So can the voltage of your battery be increased? Sure, add cell(s).

But if you've got a conventional battery, all in one case? Time to ante up and replace it. Screwing around with kludge jobs will be an ultimate waste of time and money. And the concept of adding a resistor in order to increase voltage, if I may be blunt, says that you really might want to have an electrician check over the entire system when you do that. Resistors never increase voltage, they only lower it. Chosen improperly (wrong wattage rating) they can be good heating elements, and start a fire. Or explode like a blown fuse.
A "car" battery can put out over 3000 amps into a dead short. If that short is through your wedding ring, metal watchband, wrench in hand...you can get seriously injured. Which is why I suggest an electrician, to do things now, until you check out some books on 12-volt systems and come up to speed on them.

Low battery voltage can be from a bad battery, but it can also be a good battery being measured incorrectly, not at the terminals but somewhere else like a panel meter, which allows for bad connections, thin wiring, and other problems that show "low" voltage in the system, when the battery is OK.

Better to have a pro come in and check out the entire system, so it works properly and so you're safe with it.

If you have a 12V nominal battery at that voltage you have a bad or shorted cell. The battery is now borderline dangerous..

No bordeline about it mate you are a floating fire hazard if you use this.

'Back in the day' I used to do repairs to small L/A cells and one trick that sometimes worked was to empty the acid out and flush with distilled water before refilling. It worked if the problem was a build up of gunk in the bottem of the cell but only gave a fairly short increase in life. Handling the acid is DANGEROUS. On a boat I would not bother with any attempt to salvage batteries that I relied on for sailing.

Hi liveaboardL . Go on YouTube & subscribe to ( Knurlgnar24 ) he's a wiz at inverters electronics etc . Ask him your question , he will get back to you around 24-48hrs . A great guy answers all my questions , & i ask alot ! Remember to subscribe ! saillersteve.

A drill is a inductive load, not a pure resistor.
While it pulls 400W running, it may pull 5 times as much at 0rpm.
Check your inverter's specs. I could'nt find any inverters right now, but I have a circuit breaker here wich says:
Resistive load:1000W
Inductive load:300W

Reason:Much of the resistance in electrical motors comes from the magnetic field of the spinning motor.

.manitu

__________________Is it possible that my sole purpose in life is to act as a warning to others?

I have a battery that puts out a lot of power, but its max voltage is 10.6 volts, which isn't enough voltage to keep my inverter from cutting off while using the corded drill (about 400 watts)..................

No you cannot raise a battery's voltage. You also cannot use two batteries in series to achieve a higher voltage and then drop it with a resistor or combination of resistors. Not only would that be incredibly inefficient in this operation, you would need very large (power capacity) resistors. And unless there was a constant load on the output of the inverter you could never calculate the value for the resistors because the value to drop to the proper voltage would vary with the load of the inverter.

I don't know if you are posing this question as theory or if you are somehow confused. It would be very hard to find a battery with a 10.6 volt output and even if you found or made one, you won't be able to find anything that requires 10.6 volts to operate anyway.

I just looked into the option of Connecting some D-cell NiMH batteries in series & parallel & it would require about 35 NiMH D batteries to run the drill. Too expensive... (6 D's for $23 on ebay)
A D Battery can give 3.6A @.9V due to internal resistance, so for about 500 watt draw, it ain't happening.
If I use these 10.6v batteries, I'll make sure nothing gets hot with extended use & test everything. Thanks for those who warned me about the extra current draw, and the need for a step-up/down regulator & the problems w/ using a high-power resistor. Gosh, seemed like such a neat idea too! Great info resource here.

...If I use these 10.6v batteries, I'll make sure nothing gets hot with extended use & test everything...

It is stunts like this that result in boat fires. Even if you don't care about your own safety, what you propose is highly dangerous to your dock neighbors. Please reconsider.

__________________1st rule of yachting: When a collision is unavoidable, aim for something cheap.
"whatever spare parts you bring, you'll never need"--goboatingnow
"Id rather drown than have computers take over my life."--d design

Whilst a bad battery should be replaced, everyone has assumed that the low voltage has been measured at the battery. Has it? Inverters draw a lot of amps and under sized wiring will cause significant voltage drops. Other solutions are check your inverter manual to see if it has a low voltage cutout override or buy a cordless drill and use the inverter to run the battery charger.